@Art James Here in Houston I for sure aerate twice a year, especially since my home is only 2 years old and I'm trying to remediate the carnage that's left after a builder leaves the lot. Hopefully, I can get that down to once per year in the future.
When I aerate in the spring (last weekend in fact) I do a very light top-dress with leaf mold compost just to get some good organics down into the soil early on.
Then, once the real growth is pushing in the summer heat I'll aerate and top-dress with sand. I also throw down some fert right before sand and then water steady and the recovery is amazing. The picture below was too much, too soon in the year in my opinion. It took far too long to recover, because it hadn't built enough growth "momentum"
I learned from experience that while the Bermuda will definitely recover from an early spring sand leveling, it takes much longer than when it's in prime growing conditions in the summer. I woke up yesterday to 40 degrees and while the yard is green and looks good, it's barely stretched it's legs for the season!
As far as aeration, I agree with some of the previous comments. Get a good, heavy machine from the rental house. Make a double pass (you'll run out of energy before you can do too much damage to your yard, those things are punishers to the lower back). Then, do your top-dress of choice.
Here's a link for the product I use from a local yard for my organic treatment in the spring, there may be something similar available near you - https://thegroundup.com/leafmoldcompost
Good luck!